A critical requirement in the consensus-based simultaneous arrival problem is that consensus on the ETA must be achieved before any actual arrivals. Thus, the convergence rate of the consensus algorithm is important. When velocity constraints exist, however, finding the convergence rate of continuous-time algorithms is challenging. To address constrained consensus, we present a continuous-time projection-based consensus protocol for UAVs to achieve an agreement on the ETA. We show the ε-convergence of the constrained consensus algorithm and derive the convergence rate. Based on these results, a sufficient condition is provided that guarantees the feasibility for simultaneous arrival, in terms of the length of the paths as well as the UAVs' minimal and maximal velocity.
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